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Signal Processing, IEEE Transactions on

Issue 12 • Date Dec. 1996

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Displaying Results 1 - 25 of 31
  • List of reviewers

    Page(s): 3178 - 3181
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    Freely Available from IEEE
  • 1996 Index IEEE Transactions on Signal vol. 44

    Page(s): 1 - 42
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    Freely Available from IEEE
  • A global optimization technique for statistical classifier design

    Page(s): 3108 - 3122
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    A global optimization method is introduced that minimize the rate of misclassification. We first derive the theoretical basis for the method, on which we base the development of a novel design algorithm and demonstrate its effectiveness and superior performance in the design of practical classifiers for some of the most popular structures currently in use. The method, grounded in ideas from statistical physics and information theory, extends the deterministic annealing approach for optimization, both to incorporate structural constraints on data assignments to classes and to minimize the probability of error as the cost objective. During the design, data are assigned to classes in probability so as to minimize the expected classification error given a specified level of randomness, as measured by Shannon's entropy. The constrained optimization is equivalent to a free-energy minimization, motivating a deterministic annealing approach in which the entropy and expected misclassification cost are reduced with the temperature while enforcing the classifier's structure. In the limit, a hard classifier is obtained. This approach is applicable to a variety of classifier structures, including the widely used prototype-based, radial basis function, and multilayer perceptron classifiers. The method is compared with learning vector quantization, back propagation (BP), several radial basis function design techniques, as well as with paradigms for more directly optimizing all these structures to minimize probability of error. The annealing method achieves significant performance gains over other design methods on a number of benchmark examples from the literature, while often retaining design complexity comparable with or only moderately greater than that of strict descent methods. Substantial gains, both inside and outside the training set, are achieved for complicated examples involving high-dimensional data and large class overlap View full abstract»

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  • Optimal linear detectors for additive noise channels

    Page(s): 3079 - 3084
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    In an attempt to gain insight into the design of linear detectors for additive white noise channels (discrete-time case), we describe several procedures, both optimal and suboptimal. Using the Wiener representation for nonlinear systems, we derive an ad hoc suboptimal design procedure. Exact designs are found when the noise amplitude's probability distribution is stable and when the noise is Laplacian. Considering all the linear detectors thus derived, no general form for the optimal linear detector's unit-sample response becomes apparent. Performance analyses and simulations indicate substantial performance losses occur when linear detectors are used instead of optimal (likelihood ratio) ones View full abstract»

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  • Time-varying filters and filter banks: some basic principles

    Page(s): 2971 - 2987
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    We study the fundamentals of time-varying filter banks (TVFB). Using a polyphase approach to TVFBs, we are able to show some unusual properties that are not exhibited by the conventional LTI filter banks. For example, we can show that for a perfect reconstruction (PR) TVFB, the losslessness of analysis bank does not always imply that of the synthesis bank, and replacing the delay z-1 in an implementation of a lossless linear time-variant (LTV) system with z-L for integer L in general will result in a nonlossless system. Moreover, we show that interchanging the analysis and synthesis filters of a PR TVFB will usually destroy the PR property, and a PR TVFB in general will not generate a discrete-time basis for l2. Furthermore, we show that we can characterize all TVFBs by characterizing multi-input multi-output (MIMO) LTV systems. A useful subclass of LTV systems, namely the lossless systems, is discussed in detail. All lossless LTV systems are invertible. Moreover, the inverse is a finite impulse response (FIR) if the original lossless system is an FIR. Explicit construction of the inverses is given. However, unlike in the LTI case, we show that the inverse system is not necessarily unique or invertible. In fact, the inverse of a lossless LTV system is not necessarily lossless. Depending on the invertibility of their inverses, the lossless systems are divided into two groups: (i) invertible inverse lossless (IIL) systems and (ii) noninvertible inverse lossless (NIL) systems. We show that an NIL PR TVFB will only generate a discrete-time tight frame with unity frame bound. However if the PR FB is IIL, we have an orthonormal basis for l2 View full abstract»

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  • Adaptive beamforming for satellite communication with selective earth coverage and jammer nulling capability

    Page(s): 3162 - 3166
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    An algorithm has been developed to control the antenna array beam pattern for satellite communication applications where the uplink received antenna is desired to provide beamforming capability for selective earth coverage and jamming protection. The problem can be formulated to determine the antenna weight to meet the user gain and jammer null requirements in their known directions, subject to the norm bound constraint of the weight. The algorithm makes use of the orthogonal decomposition of the weight vector and a recursive procedure that provides flexibility in the determination of the constraint vectors, the constraint order, and the constraint phase optimization View full abstract»

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  • The discrete Laguerre transform: derivation and applications

    Page(s): 2925 - 2931
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    The discrete Laguerre transform (DLT) belongs to the family of unitary transforms known as Gauss-Jacobi transforms. Using classical methodology, the DLT is derived from the orthonormal set of Laguerre functions. By examining the basis vectors of the transform matrix, the types of signals that can be best represented by the DLT are determined. Simulation results are used to compare the DLT's effectiveness in representing such signals to that of other available transforms in applications such as data compression and transform-domain adaptive filters View full abstract»

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  • Efficient implementation of Koilpillai-Vaidyanathan pseudo quadrature mirror filter (PQMF) banks

    Page(s): 3135 - 3138
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    An efficient implementation algorithm for the Koilpillai-Vaidyanathan (see ibid., vol.41, no.1, p.82-92, 1993) pseudo quadrature mirror filter (KVPQMF) bank, which is useful in audio compression schemes, is presented. The implementation employs a polyphase system with discrete cosine transforms (DCTs). Theoretical and practical results show a typical saving in computational load of 82% over the direct implementation View full abstract»

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  • A theorem in probability and its applications in multidimensional signal processing

    Page(s): 3167 - 3169
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    In this correspondence, we present a result in probability that does not exist in the literature of probability theory. We show one application of this theorem in multidimensional signal processing, which generalizes some of the existing results View full abstract»

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  • Fast design of 2-D linear-phase complex FIR digital filters by analytical least squares method

    Page(s): 3157 - 3161
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    Two-dimensional full-plane and half-plane filters are more general, and much better frequency responses can be obtained than the quarter-plane filters. In this correspondence, the analytical least squares method is generalized and extended for designing 2-D full-plane and half-plane linear phase complex FIR digital filters. The 2-D filter's coefficients can be effectively determined by use of a closed-form transformation matrix and some simple element functions. The unique advantage of this technique is that it is very fast without employing iterative optimization procedures and matrix inversions. Design examples are presented to illustrate the simplicity and efficiency of the proposed method View full abstract»

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  • Wigner-based formulation of the chirplet transform

    Page(s): 3129 - 3135
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    Using the Wigner distribution, we derive and analyze a matrix formulation for the chirplet transform, a signal analysis tool that generalizes the wavelet and short-time Fourier transforms. The formulation expresses the translations, scalings, and shears of the chirplet transform in terms of affine matrix transformations on the time-frequency plane. Our approach leads naturally to several new signal transforms, which we derive, analyze, and extend View full abstract»

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  • Transform domain adaptive linear phase filter

    Page(s): 3142 - 3146
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    Describes a new adaptive linear-phase filter whose weights are updated by the normalized least-mean-square (LMS) algorithm in the transform domain. This algorithm provides a faster convergence rate compared with the time domain linear phase LMS algorithm. Various real-valued orthogonal transforms are investigated such as the discrete cosine transform (DCT), discrete Hartley transform (DHT), and power of two (PO2) transform, etc. By using the symmetry property of the transform matrix, an efficient implementation structure is proposed. A system identification example is presented to demonstrate its performance View full abstract»

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  • Linear independence of steering vectors of an electromagnetic vector sensor

    Page(s): 3099 - 3107
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    We investigate linear independence of steering vectors of one electromagnetic vector sensor. We show that every three steering vectors with distinct directions of arrival (DOAs) are linearly independent. We also show that four steering vectors with distinct DOAs are linearly independent if the ellipticity angles of the signals associated with any two of the four steering vectors are distinct. Moreover, every four steering vectors corresponding to circularly polarized signals with the same spin direction are linearly dependent. We then establish that five steering vectors are linearly independent if exactly two or three of them correspond to circularly polarized signals with the same spin direction. Finally, we demonstrate that given any five steering vectors, then for any DOA there exists a steering vector that is linearly dependent on the five steering vectors View full abstract»

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  • Optimal quadratic detection and estimation using generalized joint signal representations

    Page(s): 3031 - 3043
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    Time-frequency analysis has significant advances in two main directions: statistically optimized methods that extend the scope of time-frequency-based techniques from merely exploratory data analysis to more quantitative application and generalized joint signal representations that extend time-frequency-based methods to a richer class of nonstationary signals. This paper fuses the two advances by developing optimal detection and estimation techniques based on generalized joint signal representations. By generalizing the statistical methods developed for time-frequency representations to arbitrary joint signal representations, this paper develops a unified theory applicable to a wide variety of problems in nonstationary statistical signal processing View full abstract»

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  • Circular implementation of vector-channel lattices

    Page(s): 3147 - 3149
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    Discusses the circular (or periodic) implementation of vector-channel least-squares lattice filters. The resulting algorithm eliminates matrix inversions and greatly reduces matrix multiplications. Complete residual and AR coefficient algorithms are provided, as well as initialization and other implementation issues. A full treatment of the prediction error form of the lattices and its relationship to the residual form is also included View full abstract»

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  • Temporal and spatial sampling influence on the estimates of superimposed narrowband signals: when less can mean more

    Page(s): 3085 - 3098
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    This paper addresses the influence that the sampling locations have on the estimated frequencies of superimposed sinusoids. This problem has application in harmonic time-series analysis or direction-finding phased-array systems. Generalized mathematical bounds are developed in terms that are independent of the array locations and have an intuitively appealing physical interpretation. They establish the influence of the sampling locations on the variance of the frequency estimate and the limit at which two sources can be resolved using signal subspace estimators. For the resolution criteria, an expression dominated by the fourth central moment of the sensor locations expresses the resolving ability of the sensing array, irrespective of the array aperture or number of sensors. Increasing the fourth central moment increases an array's resolution ability. The commonly accepted notion that resolution necessarily depends on the array aperture is misleading and, indeed, that fewer snapshots from a reduced aperture array can outperform a larger array of more elements. For the estimator variance criteria, it is found that the product of the number of sensors and the second central moment (array variance) characterizes the estimator variance lower bound. The metrics developed demonstrate that the sampling topology is itself an important factor in determining the performance of the sampling system (and not the covariance lags sampled or the aperture spanned). Simulations are used to describe the results View full abstract»

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  • Maximum likelihood parameter and rank estimation in reduced-rank multivariate linear regressions

    Page(s): 3069 - 3078
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    This paper considers the problem of maximum likelihood (ML) estimation for reduced-rank linear regression equations with noise of arbitrary covariance. The rank-reduced matrix of regression coefficients is parameterized as the product of two full-rank factor matrices. This parameterization is essentially constraint free, but it is not unique, which renders the associated ML estimation problem rather nonstandard. Nevertheless, the problem turns out to be tractable, and the following results are obtained. An explicit expression is derived for the ML estimate of the regression matrix in terms of the data covariances and their eigenelements. Furthermore, a detailed analysis of the statistical properties of the ML parameter estimate is performed. Additionally, a generalized likelihood ratio test (GLRT) is proposed for estimating the rank of the regression matrix. The paper also presents the results of some simulation exercises, which lend empirical support to the theoretical findings View full abstract»

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  • Optimal decorrelating receivers for DS-CDMA systems: a signal processing framework

    Page(s): 3044 - 3055
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    Code division multiple access (CDMA) schemes allow a number of asynchronous users to share a transmission medium with minimum cooperation among them. However, sophisticated signal processing algorithms are needed at the receiver to combat interference from other users and multipath effects. A discrete-time multirate formulation is introduced for asynchronous CDMA systems, which can incorporate multipath effects. This formulation reveals interesting links between CDMA receivers and array processing problems. In this framework, linear receivers are derived that can completely suppress multiuser interference (decorrelating receivers). A criterion is introduced, which guarantees the decorrelating property, while providing optimal solutions in the presence of noise. Parametric FIR designs as well as nonparametric solutions are delineated, and their performance is analyzed. The proposed receivers are resistant to near-far effects and do not require the estimation of the users' and noise powers View full abstract»

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  • Blind identification of digital communication channels with correlated noise

    Page(s): 3154 - 3156
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    Blind identification consists of estimating the impulse response of a linear, time-invariant channel used for transmission of digital data by observing the channel output without knowledge of the transmitted symbol sequence. We show how a previously proposed algorithm (Moulines et al., 1995) based on second-order statistics of the received signal can be modified to account for correlated noise View full abstract»

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  • A new method for efficient convolution in frequency domain by nonuniform partitioning for adaptive filtering

    Page(s): 3123 - 3129
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    By using block processing, partitioning, and fast Fourier transforms (FFTs), large filters perform efficiently in the frequency domain. For small processing delay the complexity can still be too large for implementation on a digital signal processor (DSP). A solution is to partition the filter into unequal-length subfilters. Application in adaptive filtering yields the nonuniform partitioned block frequency domain adaptive filter (NU-PBFDAF) View full abstract»

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  • Variable-block-size lapped transforms

    Page(s): 3139 - 3142
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    A structure for implementing lapped transforms with time-varying block sizes that allows full orthogonality of the transient transforms is presented. The formulation is based on a factorization of the transfer matrix into orthogonal factors. Such an approach can be viewed as a sequence of stages with variable-block-size transforms separated by sample-shuffling (delay) stages. Details and design examples for a first-order system are presented View full abstract»

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  • Low-rank adaptive filters

    Page(s): 2932 - 2947
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    We introduce a class of adaptive filters based on sequential adaptive eigendecomposition (subspace tracking) of the data covariance matrix. These new algorithms are completely rank revealing, and hence, they can perfectly handle the following two relevant data cases where conventional recursive least squares (RLS) methods fail to provide satisfactory results: (1) highly oversampled “smooth” data with rank deficient of almost rank deficient covariance matrix and (2) noise-corrupted data where a signal must be separated effectively from superimposed noise. This paper contradicts the widely held belief that rank revealing algorithms must be computationally more demanding than conventional recursive least squares. A spatial RLS adaptive filter has a complexity of O(N2) operations per time step, where N is the filter order. The corresponding low-rank adaptive filter requires only O(Nr) operations per time step, where r⩽N denotes the rank of the data covariance matrix. Thus, low-rank adaptive filters can be computationally less (or even much less) demanding, depending on the order/rank ratio N/r or the compressibility of the signal. Simulation results substantiate our claims. This paper is devoted to the theory and application of fast orthogonal iteration and bi-iteration subspace tracking algorithms View full abstract»

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  • Difference equation representation of chirp signals and instantaneous frequency/amplitude estimation

    Page(s): 2948 - 2958
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    We present a time-varying coefficient difference equation representation for sinusoidal signals with time-varying amplitudes and frequencies. We first obtain a recursive equation for a single chirp signal. Then, using this result, we obtain time-varying coefficient difference equation representations for signals composed of multiple chirp signals. We analyze these equations using the skew-shift operators. We show that the phases of the poles of the difference equations produce instantaneous frequencies (IF), and the magnitudes are proportional to the ratio of successive values of the instantaneous amplitudes (IA). Then algorithms are presented for the estimation of instantaneous frequencies and instantaneous amplitudes for multicomponent signals composed of chirps using the difference equation representation. The first algorithm we propose is based on the skew-shift operators. Next we derive the conditions under which we can use the so-called frozen-time approach. We propose an algorithm for IF and IA estimation based on the frozen-time approach. Then we propose an automatic signal separation method. Finally, we apply the proposed algorithms to single and multicomponent signals and compare the results with some existing methods View full abstract»

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  • Model based phase unwrapping of 2-D signals

    Page(s): 2999 - 3007
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    A parametric model and a corresponding parameter estimation algorithm for unwrapping 2-D phase functions are presented. The proposed algorithm performs global analysis of the observed signal. Since this analysis is based on parametric model fitting, the proposed phase unwrapping algorithm has low sensitivity to phase aliasing due to low sampling rates and noise, as well as to local errors. In its first step, the algorithm fits a 2-D polynomial model to the observed phase. The estimated phase is then. Used as a reference information that directs the actual phase unwrapping process. The phase of each sample of the observed field is unwrapped by increasing (decreasing) it by the multiple of 2π, which is the nearest to the difference between the principle value of the phase and the estimated phase value at this coordinate. In practical applications, the entire phase function cannot be approximated by a single 2-D polynomial model. Hence, the observed field is segmented, and each segment is fit with its own model. Once the phase model of the observed field has been estimated, we can repeat the model-based unwrapping procedure described earlier for the case of a single segment and a single model field View full abstract»

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  • Equivariant adaptive source separation

    Page(s): 3017 - 3030
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    Source separation consists of recovering a set of independent signals when only mixtures with unknown coefficients are observed. This paper introduces a class of adaptive algorithms for source separation that implements an adaptive version of equivariant estimation and is henceforth called equivariant adaptive separation via independence (EASI). The EASI algorithms are based on the idea of serial updating. This specific form of matrix updates systematically yields algorithms with a simple structure for both real and complex mixtures. Most importantly, the performance of an EASI algorithm does not depend on the mixing matrix. In particular, convergence rates, stability conditions, and interference rejection levels depend only on the (normalized) distributions of the source signals. Closed-form expressions of these quantities are given via an asymptotic performance analysis. The theme of equivariance is stressed throughout the paper. The source separation problem has an underlying multiplicative structure. The parameter space forms a (matrix) multiplicative group. We explore the (favorable) consequences of this fact on implementation, performance, and optimization of EASI algorithms View full abstract»

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Aims & Scope

IEEE Transactions on Signal Processing covers novel theory, algorithms, performance analyses and applications of techniques for the processing, understanding, learning, retrieval, mining, and extraction of information from signals

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Editor-in-Chief
Zhi-Quan (Tom) Luo
University of Minnesota